Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지

Power analysis for $2{\times}2$ factorial in randomized complete block design

블럭이 존재하는 $2{\times}2$ 요인모형의 검정력 분석

  • Choi, Young-Hun (Department of Information and Statistics, Hanshin University)
  • 최영훈 (한신대학교 정보통계학과)
  • Received : 2011.01.23
  • Accepted : 2011.03.17
  • Published : 2011.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Powers of rank transformed statistic for testing main effects and interaction effects for $2{\times}2$ factorial design in randomized complete block design are very superior to powers of parametric statistic without regard to the block size, composition method of effects and the type of population distributions such as exponential, double exponential, normal and uniform. $2{\times}2$ factorial design in RCBD increases error effects and decreases powers of parametric statistic which results in conservativeness. However powers of rank transformed statistic maintain relative preference. In general powers of rank transformed statistic show relative preference over those of parametric statistic with small block size and big effect size.

블럭이 존재하는 $2{\times}2$ 요인모형의 주 효과 및 상호작용효과를 검정하기 위한 순위변환 통계량의 검정력은 블럭크기, 효과들의 구성방법 및 지수분포, 이중지수분포, 정규분포, 균일 분포를 포함한 모든 모집단 분포하에서 모수적 통계량의 검정력보다 월등한 우위를 보인다. 이는 블럭이 추가된 요인 모형은 블럭과 요인의 상호작용들이 오차항을 증가시켜 모수적 통계량의 검정력을 감소시키는 보수적 성향을 보이나, 순위변환 통계량의 검정력은 상대적 우위를 유지함에 기인한다고 유추할 수 있다. 일반적으로 블럭크기가 작고, 효과크기가 클수록 순위변환 통계량의 검정력은 모수적 통계량의 검정력보다 상당히 큰 격차의 상대적 우위를 보임을 알 수 있다.

Keywords

References

  1. Akritas, M. G. and Papadatos, N. (2004). Heteroscedastic one way ANOVA and lack of fit tests. Journal of the American Statistical Association, 99, 368-382. https://doi.org/10.1198/016214504000000412
  2. Choi, J. S. (2010). A mixed model for repeated split-plot data. Journal of the Korean Data & Information Science Society, 21, 1-9.
  3. Choi, Y. H. (1998). A study of the power of the rank transform test in a 2(3) factorial experiment. Communications in Statistics, 27, 251-266.
  4. Choi, Y. H. (2008). Power comparison in a balanced factorial design with a nested factor. Journal of the Korean Data & Information Science Society, 19, 1059-1071.
  5. Choi, Y. H. (2010). Rank transformation analysis for 4 x 4 balanced incomplete block design. Journal of the Korean Data & Information Science Society, 21, 231-240.
  6. Gorman, J. O. and Akritas, M. G. (2001). Nonparametric models and methods for designs with dependent censored data. Biometrics, 57, 88-95. https://doi.org/10.1111/j.0006-341X.2001.00088.x
  7. Ha, J. C. (2007). Measures of slope rotatability for mixture experiment designs. Journal of the Korean Data & Information Science Society, 18, 745-755.
  8. Hora, S. C. and Iman, R. L. (1988). Asymptotic relative efficiencies of the rank transformation procedure in randomized complete block design. Journal of the American Statistical Association, 83, 462-470. https://doi.org/10.1080/01621459.1988.10478618
  9. Kepner, J. L. and Robinson, D. H. (1988). Nonparametric methods for detecting treatment effects in repeated-measures designs. Journal of the American Statistical Association, 83, 456-461. https://doi.org/10.1080/01621459.1988.10478617
  10. Ko, J. S. (2006). Improving process stability using design of experiments. Journal of the Korean Data & Information Science Society, 17, 633-645.
  11. Park, S. G. and Jang, J. H. (2007). Assessing bioequivalence of variabilities in 2x2 crossover design. Journal of the Korean Data & Information Science Society, 18, 645-657.
  12. Pavur, R. and Nath, R. (1986). Parametric versus rank transform procedures in the two-way factorial experiment. Journal of Statistical Computation Simulation, 23, 231-240. https://doi.org/10.1080/00949658608810873
  13. Pirie, W. R. and Rauch, H. L. (1984). Simulated efficiencies of tests and estimators from general linear models analysis based on ranks: The two-way layout with interaction. Journal of Statistical Computation Simulation, 20, 197-204. https://doi.org/10.1080/00949658408810776
  14. Thompson, G, L. (1991), A note on the rank transform for interactions. Biometrika, 78, 697-701. https://doi.org/10.1093/biomet/78.3.697